I know that some of them make a squeal or a slight straining vocalization when they poop. But I've never encountered an audible 'squeak' coming from a bird's vent. You might pose the question to the avian vet when she goes in for the beak and nail trim.

My 2 GCCs do this as well. It's not exactly a squeak, almost like a barely audible pip. They are 100% healthy in every way, it's just something they do I guess. I know what you're talking about though.